Preface: Non-equilibrium transport, interfaces, and mixing in plasmas

Non-equilibrium transport, interfaces, and interfacial mixing play an important role in plasmas in high and low energy density regimes, at astrophysical and at atomic scales, and in nature and technology.¹ In supernova blasts, the interfacial mixing of materials of progenitor star provides conditions for synthesis of chemical elements with heavy atomic mass.^2,3 In the Sun, the evolution of spots and flares is strongly influenced by downdrafts-unstable finger type structures pushing the matter from the solar surface deeply in the convection zone.^4,5 In inertial confinement fusion, the shock induced mixing of hot and cold neutral plasmas can preempt the formation of hot spot.^6,7 For non-neutral plasmas, unstable interfaces are directly relevant to particle-field interactions in magnetic fusion, magneto-inertial fusion, and imploding Z-pinches.^1,7,8 They are inherent in the processes involving light–matter interaction, in the technology of plasma thrusters, and in the plasma discharges formed in and interfacing with liquids—an emerging area of plasma physics research.^9–12 While not studied in this perspective earlier interfacial mixing can be of utmost importance in the interface between wafers and the plasma above them in semiconductor etch and deposition tools.¹² Furthermore, a number of long-standing classical problems of plasma physics can be viewed in a new light as mixing, including the problem of magnetic reconnection and the topology and evolution of current sheets and magnetic flux ropes.^1–12 For instance, the breakup of current sheets into plasmoids and the magnetic reconnection that follows it serve to stir the current into a new state.^5,8 This is especially interesting when the plasma consists of several ion species, such as in the Sun and in the solar corona.⁴ 

In some of these environments (e.g., stellar interiors and plasma thrusters), non-equilibrium dynamics of interfaces and interfacial mixing are expected to be enhanced; in some others (for instance, in fusion and nano-fabrication), they should be mitigated and tightly controlled.¹ In all these circumstances, however, one needs to achieve a better understanding of fundamentals of non-equilibrium transport, interfaces, and interfacial mixing in plasmas.^1–12 

Non-equilibrium processes with interfacial mixing are exceedingly challenging to study in either neutral plasmas, which can often be viewed as fluids with special equation of state, or in non-neutral plasmas, with charged particles and electro-magnetic fields.^1–14 These processes usually involve sharp and rapid changes of the flow fields, high pressures and accelerations, and strong coupling of particles and electro-magnetic fields. They are inhomogeneous (i.e., the flow fields are essentially non-uniform, and may involve fronts), anisotropic (i.e., their dynamics depend on the directions), non-local (i.e., plasma flows may include contributions from all the scales and may sense initial and boundary conditions), and statistically unsteady (i.e., mean values of the quantities vary with time, and there are also time-dependent fluctuations around these means). Their properties often strongly deviate from those prescribed by standard scenarios of plasma dynamics at macroscopic scales and at kinetic scales.^1–14 

Despite these challenges, significant success has been recently achieved in theoretical analysis, in large-scale numerical simulations, and in experiments involving non-equilibrium transport, interfaces, and interfacial mixing in plasmas.^1–14 In theory, this includes the new analytical approaches for handling the multi-scale, non-local, and statistically unsteady dynamics, and the discoveries of new instabilities and new mechanisms for energy transport in unstable plasma flows.^2,9,14 In simulations, significant accomplishments are reported in the applications of powerful Lagrangian and Eulerian numerical methods for modeling realistic plasma processes.^4,6 In experiment, in fusion facilities, and in laboratory plasma devices remarkable progress is achieved in the possibilities for the large dynamic range, high precision, high accuracy, and the high data acquisition rate.^5–10 This success opens new opportunities for the studies of fundamental properties of non-equilibrium dynamics of interfaces and interfacial mixing in plasmas at astrophysical and at kinetic scales.^1,14

Our Special Topic presents the state-of-the-art research on non-equilibrium transport, interfaces, and interfacial mixing in plasmas.^15–20 The Issue brings together scientists working in various areas of plasma physics, including astrophysical, laboratory, and fusion plasmas. It serves to promote the exchange of ideas and to motivate the discussions of rigorous theoretical approaches and state-of-the-art numerical simulations along with advanced experimental techniques and technological applications.^15–20 This Issue is made to attract attention of professional readership of Physics of Plasmas to problems of interfaces and interfacial mixing in plasmas. It also appeals to the interdisciplinary physics community, by linking plasma physics and fundamentals of non-equilibrium dynamics.^15–20 

This Special Topic collects works that were presented at the invited mini-conference non-equilibrium transport, interfaces and mixing in plasmas at the 2019 Annual Meeting of the Division of Plasma Physics of the American Physical Society.¹⁵ The two mini-conference sessions included eighteen invited talks on the state-of-the-art research on plasmas in high and in low energy density regimes, in nature and technology, in theory, laboratory experiments, and simulations. The mini-conference lecturers and speakers were invited to contribute to the collection. The five papers were accepted.^15–20 

Lan and Kaganovich study the “Neutralization of an ion beam by electron injection,” including the excitation and the propagation of electrostatic solitary waves.¹⁶ The authors employ the state-of-the-art electrostatic particle-in-cell numerical simulations to investigate the charge neutralization of an ion beam by the electron injection. They find that the electrostatic solitary waves can be robustly generated in the process of the neutralization and can last for a long time, hence, strongly influencing the neutralization process. The important observation of this work is that electrostatic solitary waves can propagate along the axis of the ion beam, reflect from the beam boundaries, and, furthermore, can pass through each other with only small changes in amplitude.¹⁶ 

Jacobs, Gekelman, Pribyl, and colleagues present the “Experiments on plasma arcs at a water–air interface.”¹⁷ These experiments investigate the expansion of exploding water plasma and the morphology of a fireball with and without an external magnetic field. They find that the process of plasma expansion, the structure of the internal magnetic fields in the plasma bulk, and the plasma spectra are very different from in the cases free from magnetic field and with a magnetic field, which is directed along the axis of expansion and exceeds some threshold value. Remarkably, this type of experiment can serve as a platform for detailed studies of interfacial mixing and can possibly shed some light on very different plasma processes, including high energy density plasmas at high power laser facilities.¹⁷ 

Unstable interfaces and interfacial mixing govern a broad range of plasma processes in high and in low energy density regimes.^2,9,14 In theories describing these processes, the interface can be viewed as a phase boundary broadly defined. For neutral plasmas (fluids), two types of phase boundaries are usually considered—a front, which has zero mass transport across it, and an interface, through which mass can be transported.^2,14 Fronts are destabilized by accelerations, leading to Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities and RT/RM interfacial mixing.^2,21 RT/RM instabilities and RT/RM mixing play important role in the direct drive inertial confinement fusion, in the abundance of chemical elements in supernova remnants, in the fingering of interstellar media along the edges of black holes, and in the efficiency of plasma thrusters.^2,4,6,7,9,10 For interfaces, the inertial stabilization mechanism and the new fluid instability are recently discovered.¹⁴ Unstable interfaces are critical for thermonuclear flashes in type-Ia supernova, coronal mass ejections in the solar flares, downdrafts in planetary magneto-convection, and laser ablated plasmas in indirect drive inertial confinement fusion.^1,6,7

Three papers in the Special Topic focus on theoretical studies of unstable interfaces and interfacial mixing in neutral plasmas.^18–20 

Matsuoka, Nishihara, and Cobos-Campos present the analytical and numerical studies of the “Linear and nonlinear interactions between an interface and bulk vortices in the classical Richtmyer–Meshkov instability.”¹⁸ Richtmyer–Meshkov instability (RMI) is driven by a shock refracting a perturbed interface. The interfacial mixing is accompanied by vortices produced by the shock and by the shear at the interface. The authors investigate the nonlinear evolution of RMI within the vortex sheet model. Particularly, they observe that in the nonlinear stage, the interaction between the interface and the vortices strongly affects the interfacial shape and the dynamics of the bulk, whereas vortices behind the transmitted shock enhance the growth of the interface perturbations.¹⁸ 

Abarzhi and Williams apply group theory approach to investigate the scale-dependent dynamics of Rayleigh–Taylor instability (RTI) driven by variable accelerations with power-law time dependence.¹⁹ Such accelerations are typical in supernova blasts, inertial confinement fusion, and nano-fabrication. The authors solve this long-standing problem for the linear and nonlinear RTI and yield the unified framework for the scale-dependent dynamics of regular bubbles and singular spikes. This includes RTI evolution at early times, for a broad range of acceleration parameters and initial conditions, and at late times, where the family of nonlinear asymptotic solutions is found. The theory demonstrates the essentially multi-scale and interfacial character of RT dynamics and provides extensive benchmarks for future research.¹⁹ 

Ilyin and Abarzhi investigate “Macroscopic and microscopic stabilization mechanisms of unstable interface with interfacial mass flux.”²⁰ This work focuses on the interplay of the destabilizing acceleration with macroscopic stabilization inertial mechanism and microscopic surface tension and finds solutions for the stable and unstable dynamics. While the surface tension influences only the interface, its presence leads to formation of energetic in nature vortical structures in the bulk. In the unstable regime, the interface dynamics correspond to the standing wave with the growing amplitude. It has the growing interface velocity; it is the fastest for strong accelerations typical for laser ablated plasmas. This opens new venues for stabilization and control of unstable plasmas in inertial confinement fusion.²⁰ 

The significant progress, which is achieved in the theory, experiment, and numerical modeling of non-equilibrium transport, interfaces, and interfacial mixing,^15–20 can enable better understanding, and ultimately control, of complex plasmas processes in nature and technology.^1–15 

For inertial confinement fusion, the new inertial mechanism of the interface stabilization suggests that in unstable laser ablated plasmas, the growth of the interface perturbation is accompanied by the growth of the interface velocity.^14,20 This explains the quick extinction of the hot spot, which is observed in high energy density plasma experiments at the National Ignition Facility and is a challenge to model in the simulations.^6,7,22 The new theoretical benchmarks^14,20 can help to improve the methods of numerical modeling of fusion plasmas.⁶ In astrophysics, the interfacial and multi-scale character of Rayleigh–Taylor dynamics and its dependence on deterministic conditions (found in theory and observed in experiments^19,21) explain that supernovae can, indeed, be considered an astrophysical initial value problem, encapsulating the information on the entire process of stellar evolution, to be deduced from observations of supernova remnants.^2,3 The advancements in probing plasmas in experiments¹⁷ open new opportunities for explorations of properties of interfaces and interfacial mixing in plasmas and for getting knowledge on these complex processes directly from data. These advancements—the high reproducibility and affordability, the tight control of experimental parameters, and the broad range of conditions, among others—can further expand the existing approaches of plasmas flows control in high and in low energy density regimes.^5–13,22

We expect this collection of papers to explore and assess the state-of-the-art in the interfaces and mixing and their non-equilibrium dynamics in plasmas; to attract attention to plasma physics of a broad research community, including experimentalists, theoreticians, and numerical modelers; to provide some “thought food” to plasma technology; and to chart new research directions in this fundamental and actively developing research area of plasma physics (Fig. 1).